MinT - Best Known (84−37, 84, s)-Nets in Base 5

Best Known (84−37, 84, s)-Nets in Base 5

(84−37, 84, 132)-Net over F₅ — Constructive and digital

Digital (47, 84, 132)-net over F₅, using

2 times m-reduction [i] based on digital (47, 86, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 43, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(84−37, 84, 141)-Net over F₅ — Digital

Digital (47, 84, 141)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−37, 84, 3142)-Net in Base 5 — Upper bound on s

There is no (47, 84, 3143)-net in base 5, because

1 times m-reduction [i] would yield (47, 83, 3143)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 10355 158044 718909 659231 212762 938650 314171 612944 716427 142585 > 5⁸³ [i]